Surgery on a knot in $S^3$ is said to be an alternating surgery if it yields the double branched cover of an alternating link. The main theoretical contribution is to show that the set of alternating surgery slopes is algorithmically computable and to establish several structural results. Furthermore, we calculate the set of alternating surgery slopes for many examples of knots, including all hyperbolic knots in the SnapPy census. These examples exhibit several interesting phenomena including strongly invertible knots with a unique alternating surgery and asymmetric knots with two alternating surgery slopes. We also establish upper bounds on the set of alternating surgeries, showing that an alternating surgery slope on a hyperbolic knot satisfies $|p/q| \leq 3g(K)+4$. Notably, this bound applies to lens space surgeries, thereby strengthening the known genus bounds from the conjecture of Goda and Teragaito.

Metadata management for distributed data sources is a long-standing but ever-growing problem. To counter this challenge in a research-data and library-oriented setting, this work constructs a data architecture, derived from the data-lake: the metadata-lake. A proof-of-concept implementation of this proposed metadata aggregator is presented and briefly evaluated.

We investigate the ultrafast electron dynamics of a model of a wide-bandgap material with inner, valence, and conduction bands excited by an intense few-femtosecond pump and monitored by a delayed attosecond extreme-ultraviolet probe pulse. Complementary computational methods are utilized and compared, based on the semiconductor Bloch equations (SBEs) and time-dependent density functional theory (TDDFT). TDDFT is employed to study a finite-size system, while the SBEs are utilized to investigate the corresponding solid with periodic boundary conditions imposed, with the crystal-momentum-dependent energy bands and interband couplings calculated in the parallel-transport structure gauge. The resulting strong-field electron dynamics are employed to predict experimentally accessible attosecond transient absorption spectroscopy (ATAS) signals as a function of the probe-pulse frequency and pump-probe interpulse delay. Both simulation protocols similarly capture the time-delay-dependent spectral features in the ATAS signals. The very good agreement between our TDDFT and SBE-based results allows us to interpret the ab-initio TDDFT simulations in terms of SBEs' interband couplings, validating our SBE-based model and corroborating its conclusions.

A finite element (FE) discretization for the steady, incompressible, fully inhomogeneous, generalized Navier-Stokes equations is proposed. By the method of divergence reconstruction operators, the formulation is valid for all shear stress exponents $p > \tfrac{2d}{d+2}$. The Dirichlet boundary condition is imposed strongly, using any discretization of the boundary data which converges at a sufficient rate. $\textit{A priori}$ error estimates for the velocity vector field and kinematic pressure are derived and numerical experiments are conducted. These confirm the quasi-optimality of the $\textit{a priori}$ error estimate for the velocity vector field. The $\textit{a priori}$ error estimates for the kinematic pressure are quasi-optimal if $p \leq 2$.

First-nature geography shapes the location of prosperity. I provide evidence by investigating the effects when it suddenly changes. In 1825 a storm breached the Agger Isthmus. This connected Denmark's west Limfjord Region to the North Sea. I demonstrate that trade followed. Prosperity relocated with it: population rose 27.0 percent within a generation - an elasticity of 1.6 relative to market access - with occupational shifts toward fishing and manufacturing. Fertility, not migration, drove the expansion. A mirror experiment, the waterway's closure circa 1086-1208, caused symmetric declines in medieval coin and building finds.

We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical systems exhibiting the specification property. Moreover, we apply our results to study the metric mean dimension of suspension flows.

This paper proposes a novel framework to price energy storage in economic dispatch with a social welfare maximization objective. This framework can be utilized by power system operators to generate default bids for storage or to benchmark market power in bids submitted by storage participants. We derive a theoretical framework based on a two-stage chance-constrained formulation which systematically incorporates system balance constraints and uncertainty considerations. We present tractable reformulations for the joint chance constraints. Analytical results show that the storage opportunity cost is convex and increases with greater net load uncertainty. We also show that the storage opportunity prices are bounded and are linearly coupled with future energy and reserve prices. We demonstrate the effectiveness of the proposed approach on an ISO-NE test system and compare it with a price-taker storage profit-maximizing bidding model. Simulation results show that the proposed market design reduces electricity payments by an average of 17.4% and system costs by 3.9% while reducing storage's profit margins, and these reductions scale up with the renewable and storage capacity.

Clifford Taubes showed that the moduli space of the variational equation of the Yang-Mills-Higgs functional on the plane is non-empty, and its elements correspond to "vortices". Inspired by this result, in this paper, we show that the moduli space of the Hitchin-type dimensional reduction of the Seiberg-Witten equations on the plane contains both exponentially decayed solutions and polynomial growth solutions.

We use $K$-theory of the $C^*$-algebras to study the Arakelov geometry, i.e. a compactification of the arithmetic schemes $V\to Spec ~\mathbf{Z}$. In particular, it is proved that the Picard group of $V$ is isomorphic to the $K_0$-group of a Cuntz-Pimsner algebra associated to $V$. We apply the result to the finiteness problem for the algebraic varieties over number fields.

We present a modular hierarchy of private delegated quantum computation protocols tailored to user-level and industry-level settings and parameterized by the quantum resources available to the client. For each protocol, we specify the client capabilities, delegated gate set, adversarial model, transcript leakage and resulting privacy claims. The hierarchy separates QOTP state privacy under declared leakage from leakage-dependent transcript-level angle ambiguity, compiler- and leakage-function-dependent structural privacy, and output privacy, clarifies when public Clifford operations can be evaluated on quantum-one-time-pad encrypted data by classical key updates, and identifies where non-Clifford privacy, non-collusion or additional primitives are required. The classical-client branch uses a persistent common-node, matching-hidden split-QOTP together with shuffled finite-grid $r$-share sign-randomized angle sharing to obtain leakage-relative state hiding under an explicit $ε_{\mathrm{key}}$ key-hiding condition and transcript-level unlinkability under hidden-matching assumptions under an explicit non-total-collusion and leakage model. The angle-sharing primitives provide transcript ambiguity under explicit leakage assumptions, not universal blindness. The trap-based layer provides detection under stated assumptions, but it is not a stand-alone malicious-security proof.

Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that generalizes the standard notion of abstract elementary class, and show that it is an example of an accessible category. We apply our framework to show that the logic $\mathsf{FOT}$ introduced by Kontinen and Yang satisfies a version of Lindström's Theorem. Finally, we consider the problem of transferring categoricity between different cardinalities for complete theories in existential second-order logic (or independence logic) and prove both a downwards and an upwards categoricity transfer result.

Despite the importance of scientific software for research, it is often not formally recognized and rewarded. This is especially true for foundational libraries, which are hidden below packages visible to the users (and thus doubly hidden, since even the packages directly used in research are frequently not visible in the paper). Research stakeholders like funders, infrastructure providers, and other organizations need to understand the complex network of computer programs that contemporary research relies upon. In this work, we use the CZ Software Mentions Dataset to map the upstream dependencies of software used in biomedical papers and find the packages critical to scientific software ecosystems. We propose centrality metrics for the network of software dependencies, analyze three ecosystems (PyPi, CRAN, Bioconductor), and determine the packages with the highest centrality.

We introduce H-clique-width, a new structural measure of graphs that aims to provide a hereditary analogue of the traditional graph product structure. The definition naturally generalises the ordinary clique-width concept. As a result, for a class H of graphs (such as the class of paths), the H-clique-width of a graph G equals the least integer t such that G is isomorphic to an induced subgraph of the strong product of a graph from H and a graph of clique-width t. We study basic properties of H-clique-width and compare it to other established structural parameters of graphs. Notably, we prove that the celebrated Planar graph product structure theorem by Dujmovic et al., and related graph product structure results, can all be formulated with the induced subgraph containment relation. In particular, every planar graph is isomorphic to an induced subgraph of the strong product of a path and a graph of tree-width 39.

In this paper we develop a Stochastic Gradient Langevin Dynamics (SGLD) algorithm tailored for solving a certain class of non-convex distributionally robust optimisation (DRO) problems. By deriving non-asymptotic convergence bounds, we build an algorithm which for any prescribed accuracy $\varepsilon>0$ outputs an estimator whose expected excess risk is at most $\varepsilon$. As a concrete application, we consider the problem of identifying the best non-linear estimator of a given regression model involving a neural network using adversarially corrupted samples. We formulate this problem as a DRO problem and demonstrate both theoretically and numerically the applicability of the proposed robust SGLD algorithm. Moreover, numerical experiments show that the robust SGLD estimator outperforms the estimator obtained using vanilla SGLD in terms of test accuracy, which highlights the advantage of incorporating model uncertainty when optimising with perturbed samples.

We show that spin chains in thermal equilibrium have a correlation structure in which individual regions are strongly correlated at most with their near vicinity. We quantify this with alternative notions of the conditional mutual information, defined through the so-called Belavkin-Staszewski relative entropy. We prove that these measures decay superexponentially at every positive temperature, under the assumption that the spin chain Hamiltonian is translation-invariant. Using a recovery map associated with these measures, we sequentially construct tensor network approximations in terms of marginals of small (sublogarithmic) size. As a main application, we show that classical representations of the states can be learned efficiently from local measurements with a polynomial sample complexity. We also prove an approximate factorization condition for the purity of the entire Gibbs state, which implies that it can be efficiently estimated to a small multiplicative error from a small number of local measurements. The results extend from strictly local to exponentially-decaying interactions above a threshold temperature, albeit only with exponential decay rates. As a technical step of independent interest, we show an upper bound to the decay of the Belavkin-Staszewski relative entropy upon the application of a conditional expectation.

Recent advances in electron microscopy allowed the generation of high-energy electron wave packets of ultrashort duration. Here we present a non-perturbative S-matrix theory for scattering of ultrashort electron wave packets by atomic targets. We apply the formalism to a case of elastic scattering and derive a generalized optical theorem for ultrashort wave-packet scattering. By numerical simulations with 1-fs wave packets, we find in angular distributions of electrons on a detector one-fold and anomalous two-fold azimuthal asymmetries. We discuss how the asymmetries relate to the coherence properties of the electron beam, and to the magnitude and phase of the scattering amplitude. The essential role of the phase of the exact scattering amplitude is revealed by comparison with results obtained using the first-Born approximation. Our work paves a way for controlling electron-matter interaction by the lateral and transversal coherence properties of pulsed electron beams.

This paper introduces and tests an unsupervised method for detecting novel coordinated inauthentic information operations (CIOs) in realistic settings. This method uses Bayesian inference to identify groups of accounts that share similar account-level characteristics and target similar narratives. We solve the inferential problem using amortized variational inference, allowing us to efficiently infer group identities for millions of accounts. We validate this method using a set of five CIOs from three countries discussing four topics on Twitter. Our unsupervised approach increases detection power (area under the precision-recall curve) relative to a naive baseline (by a factor of 76 to 580), relative to the use of simple flags or narratives on their own (by a factor of 1.3 to 4.8), and comes quite close to a supervised benchmark. Our method is robust to observing only a small share of messaging on the topic, having only weak markers of inauthenticity, and to the CIO accounts making up a tiny share of messages and accounts on the topic. Although we evaluate the results on Twitter, the method is general enough to be applied in many social-media settings.

We prove that (logarithmic) prismatic and (logarithmic) syntomic cohomology are representable in the category of logarithmic motives. As an application, we obtain Gysin maps for prismatic and syntomic cohomology, and we explicitly identify their cofibers. We also prove a smooth blow-up formula and we compute prismatic and syntomic cohomology of Grassmannians. In the second part of the paper, we develop a descent technique inspired by the work of Nizioł~ on log $K$-theory. Using the resulting \emph{saturated descent}, we prove de Rham and crystalline comparison theorems for log prismatic cohomology, and the existence of Gysin maps for $A_{\inf}$-cohomology.

This article studies the inverse problem of recovering a nonlinearity in an elliptic equation $Δu + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first order linearization achieve this under a sign condition on $\partial_u a(x,u)$, and results based on higher order linearization recover the Taylor series of $a(x,u)$ with respect to $u$. We improve these results and show that a general nonlinearity, and not just its Taylor series, is uniquely determined up to gauge near a fixed solution. Our method is based on constructing a good solution map that locally parametrizes solutions of the nonlinear equation by solutions of the linearized equation.

We introduce predictable relative forward performance processes (PRFPP) as a new framework for studying portfolio management within a competitive and incomplete market environment. Each agent trades a distinct stock following a binomial distribution with probabilities for a positive return depending on the market regime characterized by a non-traded stochastic factor. For both the finite population and mean field games, we construct and analyse PRFPPs for initial data of the CARA class along with the associated equilibrium strategies. We find that relative performance concerns do not necessarily lead to more investment in the risky asset compared to when there are no such concerns. Under some parameter constellations, agents short a stock with positive expected excess return. The binomial market setting facilitates a straightforward adjustment of risky asset skewness, enabling an analysis of its impact on investment behavior, an aspect that continuous-time frameworks cannot capture.

Recent advances in electron microscopy trigger the question whether attosecond electron diffraction can resolve atomic-scale electron dynamics in crystalline materials in space and time. Here we explore the physics of the relevant electron-lattice scattering process in the time domain. We drive a single-crystalline silicon membrane with the optical cycles of near-infrared laser light and use attosecond electron pulses to produce electron diffraction patterns as a function of delay. For all Bragg spots, we observe time-dependent intensity changes and position shifts that are correlated with a time delay of 0.5-1.2 fs. For single-cycle excitation pulses with strong peak intensity, the correlations become nonlinear. Origin of these effects are local and integrated beam deflections by the optical electric and magnetic fields at the crystal membrane that modify the diffraction intensities in addition to the atomic structure factor dynamics by time-dependent rocking-curve effects. However, the measured time delays and symmetries allow to disentangle both effects. Future attosecond electron diffraction and microscopy experiments need to be based on these results.

Any multiplicative quiver variety is endowed with a Poisson structure constructed by Van den Bergh through reduction from a Hamiltonian quasi-Poisson structure. The smooth locus carries a corresponding symplectic form defined by Yamakawa through quasi-Hamiltonian reduction. In this note, we include the Poisson structure as part of a pencil of compatible Poisson structures on the multiplicative quiver variety. The pencil is defined by reduction from a pencil of Hamiltonian quasi-Poisson structures which has dimension $\ell(\ell-1)/2$, where $\ell$ is the number of arrows in the underlying quiver. For each element of the pencil, we exhibit the corresponding compatible symplectic or quasi-Hamiltonian structure. We comment on analogous constructions for character varieties and quiver varieties. This formalism is applied to the spin Ruijsenaars-Schneider phase space in order to explain the compatibility of two Poisson structures that have recently appeared in the literature.

We develop prismatic and syntomic cohomology relative to a $δ$-ring. This simultaneously generalizes Bhatt and Scholze's absolute and relative prismatic cohomology and shows that the latter, which was defined relative to a prism, is in fact independent of the prism structure and only depends on the underlying $δ$-ring. We give several possible definitions of our new version of prismatic cohomology: a site theoretic definition, one using prismatic crystals, and a stack theoretic definition. These are equivalent under mild syntomicity hypotheses. As an application, we note how the theory of prismatic cohomology of filtered rings arises naturally in this context.

In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this combination of uncertainty and randomness, we introduce the concept of an uncertain random variable and present a novel framework known as the linear-normal uncertain random variable. Our main focus in this work is the development of three distinct transformation techniques: the optimistic value criteria, pessimistic value criteria, and expected value criteria. These approaches allow us to convert a linear-normal uncertain random variable into a more manageable random variable. This transition facilitates the transformation from an uncertain random geometric programming problem to a stochastic geometric programming problem. Furthermore, we provide insights into an equivalent deterministic representation of the transformed geometric programming problem, enhancing the clarity and practicality of the optimization process. To demonstrate the effectiveness of our proposed approach, we present a numerical example.

We study a McKean-Vlasov Forward-Backward Stochastic Differential Equation (FBSDE) in connection with the theory of Stochastic Differential Mean-Field games, particularly the weak (non-fully coupled) formulation described in Section 3.3.1 of the book "Probabilistic theory of mean field games with applications" by Carmona and Delarue. Our main goal is to obtain regularity results for this McKean-Vlasov FBSDE, specifically classical and Malliavin differentiability

This paper examines whether repeated payday loan use, commonly known as the debt trap, harms borrowers' financial wellbeing. Using Open Banking data from 1,815 UK borrowers observed between 2017 and 2018, we model borrowing intensity using a two-state hidden Markov model (HMM). The HMM outperforms single-regime alternatives and identifies two distinct borrowing patterns: occasional (low-intensity) and persistent (high-intensity) use. Each regime exhibits a characteristic relationship between borrowing intensity and wider transaction behaviour. We translate the decoded state sequence into a practical monitoring rule based on sustained high-intensity exposure. Defining a trigger event as 12 consecutive weeks in the high-intensity regime, we find that 36.4% of borrowers experience at least one such event. Among those who do, high-intensity weeks represent 17.8% of all borrower-week observations on average. Together, these results provide evidence for a persistent high-intensity borrowing pattern and demonstrate that it can serve as a simple, interpretable rule for monitoring prolonged reliance on payday loans.

The observation of neutrino oscillations and masses motivates the extension of the standard model with right handed neutrinos, leading to heavy neutrino states possibly in the electroweak scale, which could be impacted by new high-scale weakly coupled physics. A systematic tool for studying these interactions is the neutrino-extended standard model effective field theory $ν$SMEFT. In this work we study the prospects of the future LHeC electron-proton collider to discover or constrain the $ν$SMEFT interactions, performing the first dedicated and realistic analysis of the well known lepton-trijet signals, both for the lepton flavor violating $p ~ e^{-} \rightarrow μ^{-} + 3 \mathrm{j}$ (LFV) and the lepton number violating $p ~ e^{-} \rightarrow μ^{+} + 3 \mathrm{j}$ (LNV) channels, for HNLs masses in the electroweak scale range: $100 ~\rm GeV \leq m_N \leq 500 ~\rm GeV$. The obtained sensitivity prospects show that the LHeC with $100 ~\rm fb^{-1}$ luminosity could be able to probe the scenario of a heavy $N$ and constrain the effective couplings to a region of the parameter space as tight as the bounds that are currently considered for the $\mathcal{O}(10)$GeV scale masses, with effective couplings of $\mathcal{O}(10^{-1})$ for NP scale $Λ=1 \rm TeV$.

We have developed a microspectroscopy technique for measuring gate-modulated reflectance to probe excitonic states in two-dimensional transition metal dichalcogenides. Successfully observing excited states of excitons from cryogenic to room temperature showed that this method is more sensitive to excitonic signals than traditional reflectance spectroscopy. Our results demonstrated the potential of this reflectance spectroscopy method in studying exciton physics in two-dimensional transition metal dichalcogenides and their heterostructures.

The NEPv approach has been increasingly used lately for optimization on the Stiefel manifold arising from machine learning. General speaking, the approach first turns the first order optimality condition, also known as the KKT condition, into a nonlinear eigenvalue problem with eigenvector dependency (NEPv) or a nonlinear polar decomposition with orthogonal factor dependency (NPDo) and then solve the nonlinear problem via some variations of the self-consistent-field (SCF) iteration. The difficulty, however, lies in designing a proper SCF iteration so that a maximizer is found at the end. Currently, each use of the approach is very much individualized, especially in its convergence analysis to show that the approach does work or otherwise. In this paper, a unifying framework is established. The framework is built upon some basic assumptions. If the basic assumptions are satisfied, globally convergence is guaranteed to a stationary point and during the SCF iterative process that leads to the stationary point, the objective function increases monotonically. Also a notion of atomic functions is proposed, which include commonly used matrix traces of linear and quadratic forms as special ones. It is shown that the basic assumptions are satisfied by atomic functions and by convex compositions of atomic functions. Together they provide a large collection of objectives for which the NEPv/NPDo approach is guaranteed to work.

We contribute to an uncertainty quantification problem in imaging that evaluates a hypothesis test questioning the existence of local "artefacts" appearing in the maximum a posteriori (MAP) estimate (obtained from standard numerical tools). Such a method, called Bayesian uncertainty quantification by optimization (BUQO), was introduced a few years ago as an efficient and scalable alternative to sampling methods when per-pixel error-bars are not needed. BUQO formulates a hypothesis test for probing the existence of local structures in the MAP estimate as a minimization problem, that can be solved efficiently with standard optimization algorithms. In this context, BUQO requires a "mathematical" definition of the "local artefact". This definition can be interpreted as an inpainting of the structure. However, only simple hand-crafted techniques have been proposed so far due to the complexity of the problem. In this work, we propose a data-driven alternative to BUQO where the inpainting procedure in the algorithm is performed using a convolutional inpainting neural network (NN). This results in a plug-and-play algorithm, based on the primal-dual Condat-Vu iterations,where the inpainting procedure is performed with a NN. The proposed approach is assessed on two image reconstruction problems inspired by medicine. We specifically perform simulations on two Fourier undersampling problems (discrete and non-uniform) encountered in magnetic resonance imaging, as well as a computed tomography problem using the Radon measurement operator.